Monday, April 15, 2013

PROOF: Math for Non-Majors

In a way, playwright David Auburn admits, mathematics is the MacGuffin of his play Proof. A MacGuffin (now in New York Times-approved spelling as “maguffin”) is what Alfred Hitchcock called the object that everybody in a movie or other story is concerned about—the object that drives the story, but in the end it doesn’t really matter much what it is. It could be the secret weapon, the purloined papers, the Maltese Falcon. It’s basically an excuse for character conflicts and interaction, plot twists and chase scenes.

Gwyneth Paltrow and Anthony Hopkins in the movie version of PROOF

Auburn wanted to write about two sisters in conflict over something their father left behind. Eventually he chose a mathematical proof, one that would make its author instantly famous.
But in the play it’s the authorship of the proof that’s the MacGuffin. When London production director John Madden asked audience members at intermission who they thought wrote the proof, about half said Catherine, and half said Robert.

Part of the reason Auburn choose a math proof was that mathematicians are one of the few kinds of scientists that can still work alone, so coming up with a proof that nobody else knows about is credible.
Auburn himself didn’t get past freshman calculus, but the University of Chicago requires “the Core,” a general education curriculum that comprises about a third of the undergraduate class load. It was the Core, Auburn said, that gave him the “basic belief I could teach myself enough about a strange subject to say something interesting about it, and to dramatize it convincingly.”

He was also somewhat familiar with math culture. “I knew a lot of science and math guys in school,” he told the New York Times. “You’d go to the gym and you’d hear them talking pure math talk—locker room talk, University of Chicago style.”

He also wanted to address some misconceptions.
“I was always a little annoyed that, in some other depictions of the lives of scientists and mathematicians, their accomplishments were presented as somehow magical, products of pure inspiration requiring no hard work. I wanted to make sure in Proof that I emphasized the sloggy, dogged effort that goes into this stuff.”

Russell Crowe plays John Nash
in A Beautiful MInd

But math supplied another element of the story he wanted to tell—about a daughter who was afraid she was inheriting her father’s mental illness. Apart from the abstract concepts and specialized language that can make mathematicians sound crazy to outsiders, there were cases of mental illness—most notably John Forbes Nash, the mathematician who was diagnosed as a paranoid schizophrenic. He is the subject of the book and movie A Beautiful Mind, neither of which existed when Auburn began writing Proof, though he knew Nash's basic story.

But Nash’s genius, like Robert’s in the play, made important contributions to several fields (from biology and market economics to robotics,) and like Robert, he believed he was receiving secret messages only he could decipher.

(To make matters more confusing, Russell Crowe plays Nash in A Beautiful Mind, but also stars in another movie called Proof of Life, which is completely unrelated to the Auburn play.)

Auburn researched mathematicians and the math world (especially in A Mathematician’s Apology by G. H. Hardy) but he said a key decision in writing the play was deciding how much math to include. Eventually he included very little. He has Catherine and Robert talk about prime numbers, and about the “Germain primes,” a type of prime number discovered by Sophie Germain, one of the few prominent women in mathematics history. But it turns out that the largest known Germain prime that Catherine names may not actually be the largest.

Auburn does make a point of the prejudice against women in math, based on history. A critique of the play by contemporary mathematicians however suggests that this has changed in the last decade or two.
Another fear among the young characters is that in their mid-20s, they are over the hill in math breakthroughs. The mathematicians cited also note that while the boldest insights do seem to occur in the 20s and 30s, mathematicians can remain creative and productive into their 70s.

But in the end, the proof is a MacGuffin. The relevant world is academic—the anxiety over career and accomplishment. It’s also about the permutations of personalities and emotions in love relationships and especially in families. Which itself gets very quickly way beyond the higher math.